9
On the warped geometry Randall-Sumdrum background Planck (y=0)TeV (y=L) How does the background change the neutrino mass ?

10
By the usual KK expansion, … It is hard to perform seesaw diagonalization

11
The equations for the bulk propagator the warped effect is vanishing away at the low-energy limit Alternative to the KK expansion ⇒ 5D propagator

12
The result is ・ The neutrino mass is not much affected by the background ・ The result is the same for more general metric ・ The seesaw mass can be calculated without knowing the KK expansion Even with a complicated backgroud where a suitable KK expansion cannot be find, the seesaw neutrino mass is calculable.

13
Flavor symmetry breaking at the boundaries S 4 group Irreducible representations: Exmaple of the triplet S 4 breaking boundary conditions elements of the S4 group